Solve for $x$, $ \dfrac{x + 10}{4x + 16} = \dfrac{7}{x + 4} + \dfrac{1}{x + 4} $
Answer: First we need to find a common denominator for all the expressions. This means finding the least common multiple of $4x + 16$ $x + 4$ and $x + 4$ The common denominator is $4x + 16$ The denominator of the first term is already $4x + 16$ , so we don't need to change it. To get $4x + 16$ in the denominator of the second term, multiply it by $\frac{4}{4}$ $ \dfrac{7}{x + 4} \times \dfrac{4}{4} = \dfrac{28}{4x + 16} $ To get $4x + 16$ in the denominator of the third term, multiply it by $\frac{4}{4}$ $ \dfrac{1}{x + 4} \times \dfrac{4}{4} = \dfrac{4}{4x + 16} $ This give us: $ \dfrac{x + 10}{4x + 16} = \dfrac{28}{4x + 16} + \dfrac{4}{4x + 16} $ If we multiply both sides of the equation by $4x + 16$ , we get: $ x + 10 = 28 + 4$ $ x + 10 = 32$ $ x = 22 $